Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/311904 
Year of Publication: 
2022
Citation: 
[Journal:] Theory and Decision [ISSN:] 1573-7187 [Volume:] 94 [Issue:] 4 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 693-720
Publisher: 
Springer US, New York, NY
Abstract: 
The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued monotones in terms of separating families of increasing sets to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces.
Subjects: 
Multi-utility representation
Richter–Peleg function
Injective monotone
Majorization
Uncertainty preorder
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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